Yes you can cancel the Quinn policy and arrange cover elsewhere. Be careful, as Quinn will apply cancellation charges which you will need to pay. Also if you are only part way into the Quinn policy, you would not gain any no claims discount for that policy period. Make sure any quotes obtained are using the correct no claims discount.
Yes you can cancel straightaway and arrange elsewhere. Quinn may ask you to post back the certificate of Insurance. Quinn may also ask you to pay the relevant cancellation charges when you call them. I don't think Quinn wait for the certificate to come back before cancelling, but they may ask that you whether you have Insured the vehicle elsewhere, as Insurance is a legal requirement.
I would suggest that you phone Quinn to find out the cancellation process and costs. You don't want to arrange cover elsewhere and then realise you can't afford to pay Quinn their cancellation charges.
Nb. To the OP and anyone viewing this post. It may have worked out cheaper to have arranged a learners Car Insurance e.g collingwood learners and then to have switched to a normal Car Insurance upon gaining a full license. Usually if you take out a normal Car Insurance and then amend the policy mid term to a full license, it costs more. Also because of the cancellation charges, you feel like you being held to ransom. i.e can't afford to pay the charges and arrange a policy elsewhere.